Model parameter estimation device and method

Abstract

This model parameter estimation device comprises: a state amount calculation unit (332) for calculating the state amount which indicates the state of a storage battery (1) with respect to a measurement value of current, on the basis of a state equation obtained by inputting a value to a non-linear parameter (φ) of a model which represents the storage battery (1) by using the non-linear parameter (φ) and a linear parameter (ψ), and of time-series data of current and terminal voltage of the storage battery (1); a linear parameter estimation unit (333) for estimating a linear parameter (ψ) which minimizes an error between a measurement value of the terminal voltage and an estimation value of the terminal voltage calculated on the basis of the model, the state amount, and the measurement value of the current; and a non-linear parameter update unit (331) for repeating updates of the value of the non-linear parameter (φ) until the value satisfies the convergence condition such that the minimized error becomes small.

Description

[Technical field]

[0001] The present application relates to a model parameter estimation device and a model parameter estimation method. [Background technology]

[0002] In order to reduce the burden on the environment, stationary energy storage systems that utilize renewable energy are becoming more widespread. In addition, electric vehicles such as EVs (Electric Vehicles), HEVs (Hybrid Electric Vehicles), and PHVs (Plug-in Hybrid Vehicles) are being put to practical use, and the development of electric aircraft and other vehicles is also progressing.

[0003] On the other hand, these devices use storage batteries such as lithium-ion batteries, but it is known that the deterioration of storage batteries progresses with use, resulting in a decrease in performance. Therefore, there is a demand for model parameter estimation technology to model storage batteries with high accuracy, in order to estimate the SOC (State of Charge), diagnose deterioration, and predict the lifespan of storage batteries with high accuracy.

[0004] Therefore, a model parameter estimation technique using a continuous-time system identification method based on the output error method has been proposed (see, for example, Patent Document 1). Specifically, a nonlinear optimization method is applied to time-series data of current and voltage during charging and discharging of a storage battery, and model parameters are estimated so that the output voltage of a storage battery model constructed as a continuous-time system matches the measured voltage. According to this method, by appropriately selecting the initial estimation value, it is possible to estimate the model parameters with high accuracy while taking into account the nonlinearity of the OCV (Open Circuit Voltage) characteristics. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] JP 2014-86313 A (paragraphs 0017-0018, FIG. 1, paragraphs 0044-0045, FIG. 5) Summary of the Invention [Problem to be solved by the invention]

[0006] However, in the method proposed in Patent Document 1, it is necessary to set initial values ​​for all parameters prior to estimation, but depending on how the initial values ​​are given, the estimated values ​​may diverge or converge to a local solution different from the true value. Therefore, it is necessary to set the initial values ​​based on prior information of the target system, making it difficult to apply the method to systems with little prior information.

[0007] The present application discloses a technique for solving the above-mentioned problems, and has an object to provide a model parameter estimation device and a model parameter estimation method that are capable of estimating parameters with little information. [Means for solving the problem]

[0008] The model parameter estimation device disclosed in the present application uses nonlinear parameters and linear parameters. Target System A state equation obtained by substituting values ​​for the nonlinear parameters for a state space model expressing the above, Target System of input and output Based on the time series data of each measurement, input The above for the measured value Target System a state quantity calculation unit for calculating a state quantity indicating a state of the state space model, the state quantity, and the input Calculated based on the measured value of output The estimated value of output a linear parameter estimation unit that estimates the linear parameters that minimize an error between the measured value of the linear parameter and the measured value of the nonlinear parameter, and a nonlinear parameter update unit that repeatedly updates the values ​​of the nonlinear parameters until a predetermined convergence condition is satisfied so that the minimized error becomes small.

[0009] The model parameter estimation method disclosed in the present application uses nonlinear parameters and linear parameters. Target System a step of setting initial values ​​of the nonlinear parameters of a state space model expressing the above-mentioned, a state equation obtained by substituting values ​​for the nonlinear parameters of the state space model, Target System of input and output Based on the time series data of each measurement, input The above for the measured value Target System A state quantity calculation step of calculating a state quantity indicating a state of the state space model, the state quantity, and the input The above-mentioned calculated based on the measured value output The estimated value of output a linear parameter estimation step of estimating the linear parameters that minimize an error between the measured value of the linear parameter and the measured value of the nonlinear parameter, and a nonlinear parameter update step of repeatedly updating the values ​​of the nonlinear parameters until a predetermined convergence condition is satisfied so that the minimized error becomes small. Effect of the Invention

[0010] According to the model parameter estimation device or model parameter estimation method disclosed in the present application, model parameters can be estimated by setting the initial values ​​of only the nonlinear parameters, making it possible to estimate the parameters with little information. [Brief description of the drawings]

[0011] [Figure 1] 1 is a block diagram for explaining a configuration of a model parameter estimation device according to a first embodiment. [Diagram 2] 2 is a block diagram showing an example of a hardware configuration of a part that executes calculation processing of the model parameter estimation device according to the first embodiment. FIG. [Diagram 3] FIG. 2 is a diagram showing an equivalent circuit of a storage battery from which model parameters are to be estimated. [Figure 4] FIG. 13 is a diagram showing a Foster-type equivalent circuit as another model of a storage battery whose model parameters are to be estimated. [Diagram 5] 3 is a flowchart showing the operation of the model parameter estimation device or a model parameter estimation method according to the first embodiment. [Figure 6] FIG. 11 is a graph showing the changes over time in the measured voltage value, the measured current value, and the estimated current value by the model when the model parameter estimation device or the model parameter estimation method of the first embodiment is applied to a storage battery system. [Figure 7] FIG. 2 is a graph showing the relationship between the quantity of electricity and the open circuit voltage as an OCV function estimated when the model parameter estimation device or the model parameter estimation method according to the first embodiment is applied to a certain storage battery system. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0012] Embodiment 1 1 to 7 are diagrams for explaining the configuration and operation of a model parameter estimation device and a model parameter estimation method according to a first embodiment. FIG. 1 is a block diagram of a storage battery system including a storage battery that is an estimation target and the model parameter estimation device, for explaining the configuration of the model parameter estimation device. FIG. 2 is a block diagram showing an example of the hardware configuration of a part that executes the calculation processing of the model parameter estimation device.

[0013] Fig. 3 is a diagram showing an equivalent circuit that expresses a storage battery, which is a target for estimating model parameters, by a DC component and a relaxation component of an overvoltage, and Fig. 4 is a diagram showing a Foster-type equivalent circuit that expresses diffusion impedance by connecting multiple CR parallel elements in series as another model of a storage battery. And Fig. 5 is a flowchart showing the model parameter estimation operation in the model parameter estimation device, that is, the model parameter estimation method.

[0014] Furthermore, Fig. 6 is a vertically arranged diagram showing three graphs respectively indicating the time-dependent change in the measured value of the voltage of the battery, the time-dependent change in the measured value of the current of the battery, and the time-dependent change in the estimated value of the current by the model when the model parameter estimation device or the model parameter estimation method is applied to a certain battery system, with the horizontal axis indicating the common (synchronized) time, and the vertical axis indicating the measured result of the voltage, the measured result of the current, and the estimated value of the current, respectively. Also, Fig. 7 is a graph showing the amount of electricity normalized by a certain standard capacity on the horizontal axis and the open circuit voltage on the vertical axis as the OCV function estimated at this time.

[0015] Hereinafter, a model parameter estimation device and a model parameter estimation method according to embodiments of the present application will be described in detail with reference to the drawings as appropriate. Note that the same reference numerals in each drawing indicate the same or corresponding parts.

[0016] 1, a model parameter estimation device 3 according to the first embodiment is provided in a storage battery system 100 having a storage battery 1 in order to diagnose the storage battery 1. The model parameter estimation device 3 is connected to a detection unit 2 having a current detection device 21 that detects a current, which is an output characteristic of the storage battery 1, and a voltage detection device 22 that detects a voltage, and is configured to estimate model parameters of the storage battery 1.

[0017] The storage battery 1 is typically assumed to be a lithium-ion battery, but it may be other types of storage batteries such as lead-acid batteries, nickel-metal hydride batteries, nickel-cadmium batteries, and all-solid-state batteries. The storage battery 1 to be diagnosed may be a single-cell storage battery or a storage battery module in which multiple cells are connected in any combination of series and parallel connections. It may also be a pack in which modules are further connected in any combination of series and parallel connections, and it is up to the user to decide which unit to consider as a single storage battery 1.

[0018] The model parameter estimation device 3 includes a time series data acquisition unit 31 that acquires time series data of measurement values ​​from the current value I and voltage value V detected by the detection unit 2, and a model acquisition unit 32 that acquires a storage battery model and sets an initial value of a nonlinear parameter φ, which will be described later. The model parameter estimation unit 33 further includes a parameter estimation unit 33 that estimates model parameters from the time series data acquired by the time series data acquisition unit 31, the storage battery model set by the model acquisition unit 32, and the initial value of the nonlinear parameter φ. Note that, although an example in which the model acquisition unit 32 sets the initial value has been shown here, an initial value setting unit may be provided separately or within the parameter estimation unit 33 to set (or read) the initial value.

[0019] The parameter estimation unit 33 includes a nonlinear parameter update unit 331 that updates the nonlinear parameter φ, and a state quantity calculation unit 332 that calculates a state quantity of the storage battery model based on a state equation of the storage battery model when the nonlinear parameter φ is fixed. The parameter estimation unit 33 further includes a linear parameter estimation unit 333 that estimates a linear parameter ψ based on the storage battery model and the state quantity, and a determination unit 334 that determines whether the parameter estimation has converged based on a convergence determination condition.

[0020] As shown in FIG. 2, the model parameter estimation device 3 may be configured by one piece of hardware 30 including a processor 30a and a storage device 30b. Although not shown, the storage device 30b includes a volatile storage device such as a random access memory and a non-volatile auxiliary storage device such as a flash memory. Also, instead of the flash memory, a hard disk auxiliary storage device may be included. The processor 30a executes a program input from the storage device 30b. In this case, the program is input from the auxiliary storage device to the processor 30a via the volatile storage device. Also, the processor 30a may output data such as a calculation result to the volatile storage device of the storage device 30b, or may store the data in the auxiliary storage device via the volatile storage device.

[0021] That is, the functions of each unit constituting the model parameter estimation device 3, for example, the functions of the model acquisition unit 32, the state quantity calculation unit 332, the linear parameter estimation unit 333, and the nonlinear parameter update unit 331, are realized by software, firmware, or a combination thereof. The software and firmware are written as programs and stored in the storage device 30b. The processor 30a realizes the functions of each unit of the model parameter estimation device 3 by reading out the programs stored in the storage device 30b and executing the programs.

[0022] <General Description of the Technology of the Present Application> The technical contents of the model parameter estimation device 3 and the model parameter estimation method of the present application will first be described with a general problem setting in which the target is not limited to a storage battery. First, the state space model of the target system is assumed to be expressed as equation (1).

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[0024] What we want to solve here is the time interval {t k Time series input / output data {u(t k )|k=0,···,N},{y(t k )|k=0,...,N}, the objective is to find a parameter θ that minimizes the evaluation function J(θ) based on the sum of squares of the error ε between the output hat y (estimated value) of the model shown in equation (2) and the measured value y.

[0025]

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[0026] Since this is a nonlinear optimization problem, it is possible to obtain a local optimum using known nonlinear optimization techniques. For example, the gradient of the evaluation function with respect to the parameters, or the estimated output y(t k It is possible to use the Gauss-Newton method based on the gradient of the parameters (θ,θ), or the Levenberg-Marquardt method. It is also possible to use a gradient-free method, i.e., a method not based on gradient information, such as the Nelder-Mead method, and there is no limitation regarding the specific method of nonlinear optimization.

[0027] In obtaining the gradient with respect to the parameters, it is possible to use a method based on the calculation of a sensitivity equation as described in Patent Document 1. It is also possible to use a gradient approximation method using one-sided or two-sided differences, or an adjoint method by introducing an adjoint variable.

[0028] Although equation (1) describes a continuous-time state space model, the target system may be considered in discrete time. In this case, the state space model is written as equation (3).

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[0030] On the other hand, when dealing with a continuous-time system as is, it is possible to calculate the state quantity at any time from the input time-series data by applying a known numerical solution method for differential equations to the original state equation.Typically, the Euler method or the Runge-Kutta method can be used as a numerical solution method for differential equations.

[0031] However, a general issue with the output error method, which deals with nonlinear optimization problems, is that the parameter estimates are dependent on the initial values. Therefore, as mentioned in the Background Art section, if the initial values ​​of the estimated parameters are not set appropriately, a global optimal solution cannot be obtained. Therefore, we focus on the structure of the state space model in equation (1) and consider reducing the initial value dependency. First, if the model outputs are arranged vertically in chronological order, they become as shown in equation (4).

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[0033] Therefore, when the nonlinear parameter φ in equation (5) is fixed, the linear least squares solution of the linear parameter ψ is obtained by the linear least squares method as shown in equation (6). ψ(φ)=(GΤ (φ)G(φ)) -1 G Τ (φ)Y (6) Using the linear least squares solution of equation (6), the problem to be solved is transformed from the original optimization problem, which was problem P1 in equation (7), to problem P2 in equation (8).

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[0035] In other words, problem P1, which originally required estimation of both the linear parameters ψ and the nonlinear parameters φ, has been transformed into an estimation problem (problem P2) of only the nonlinear parameters φ. If the solution for the nonlinear parameters φ in problem P2 can be obtained (fixed), the solution for the linear parameters ψ can be obtained immediately by substituting this into equation (6).

[0036] Since problem P2 is also a nonlinear optimization problem, it is possible to use various known nonlinear optimization methods as described above, as in the case of solving problem P1. When problem P1 is converted to problem P2, the only estimated parameter is the nonlinear parameter φ, which has the following advantages.

[0037] First, the initial value dependency can be reduced. When solving the original problem P1, it was necessary to set the initial values ​​of all the linear parameters ψ and nonlinear parameters φ, whereas in problem P2, the linear parameters ψ are found as a linear least squares solution without any initial values. Therefore, it is possible to solve the problem by setting only the initial value of the nonlinear parameters φ. Therefore, the problem becomes simpler in terms of estimating the true values ​​of the parameters.

[0038] Secondly, the amount of calculation is reduced in the application of many nonlinear optimization methods. For example, when using a method that uses gradient information on the parameters of the model output, the size of the gradient vector or Jacobian matrix is ​​reduced because gradient information on the linear parameter ψ is no longer necessary. From another perspective, it is expected that the number of iterative calculations required until the parameters converge will be reduced by reducing the number of estimated parameters.

[0039] Third, numerical stability is improved. In general, problems such as cancellation of significant digits are likely to occur when the order of magnitude of the values ​​of the estimated parameters is significantly different. Therefore, it is expected that such problems will be less likely to occur by reducing the number of estimated parameters.

[0040] Next, specific methods for obtaining a solution will be described for the cases where the linear parameter ψ includes a linear equality constraint and where it includes both a linear equality constraint and a linear inequality constraint.

[0041] <1: When linear parameters include linear equality constraints> When the linear parameters ψ include linear equality constraints, the equality-constrained least-squares problem of the linear parameters ψ is formulated as problem P3 in equation (9).

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[0043] Here, C eq and d eq are a matrix and a vector that respectively describe the linear equality constraints for the linear parameter ψ. To solve the problem P3 using the same idea as before, we consider the subproblem SP3 of problem P3 for G = G(φ) with the nonlinear parameter φ fixed at a certain value, which is shown in equation (10).

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[0048] <2: When linear parameters include linear equality constraints and linear inequality constraints> When the linear parameters include linear equality constraints and linear inequality constraints, the inequality-constrained least-squares problem of the linear parameters is formulated as problem P4 in equation (14).

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[0051] As a method for solving the sub-problem SP4, an interior point method, a sequential quadratic programming method, etc. can be used. In this case, iterative calculation is required, but since the sub-problem SP4 is a convex optimization problem, a global optimal solution can be obtained. Of course, since the sub-problem SP3 is included in the sub-problem SP4, such a solution method using iterative calculation can also be applied to the sub-problem SP3. Therefore, in order to solve the problem P4, it is necessary to repeatedly update the nonlinear parameters using a nonlinear optimization method and calculate the linear parameters using a solution method for the convex optimization problem.

[0052] From here, specific methods for applying the nonlinear optimization method to problems P1, P3, and P4 will be explained with problem P4 as the target. Note that problems P1 and P3 are included in problem P4, so it is sufficient to explain with problem P4 as the target. In fact, problem P1 is a special case in problem P4 where there are no inequality constraints and no equality constraints. Problem P3 is also a special case in problem P4 where there are no inequality constraints.

[0053] Let ψ = ψ be the optimal solution of the linear parameter ψ for a certain nonlinear parameter φ in the subproblem SP4. * (φ), the evaluation function to be minimized in problem P4 is given by equation (16).

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[0055] ψ * Since (φ) can be obtained by solving sub-problem SP4 using the method described above, in order to solve problem P4, it is necessary to find the nonlinear parameter φ that minimizes L(φ). Below, we will explain three nonlinear optimization methods in order: the steepest descent method, which is a type of gradient method, the Gauss-Newton method, and the Nelder-Mead method, which is a gradient-free method.

[0056] <Gradient descent method> When the steepest descent method is used, the update equation for the nonlinear parameter φ is given by equation (17).

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[0058] When it is difficult to directly calculate the gradient, a one-sided difference or a two-sided difference can be used as the gradient approximation. For example, in the case of a one-sided difference, φ j Make Δ small enough j By perturbing the equation by , the partial differential can be approximately calculated as shown in equation (18).

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[0061] <Gauss-Newton method> The update formula for the Gauss-Newton method is given by (20). However, Λ(ψ) is given by (21), and ∂ hat y(t k ,φ,ψ * (φ)) / ∂φ j is the sensitivity function, i.e., a certain nonlinear parameter φ of the output estimate. j is the partial differential with respect to

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[0063] When it is difficult to directly calculate the sensitivity function, an approximation of the sensitivity function is used instead of the sensitivity function. In other words, a gradient approximation is used instead of the gradient itself. In this case, the calculation formula when using one-sided difference is, for example, Equation (22).

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[0065] <Nelder-Mead Act> For example, when using the Nelder-Mead method, the number of iterations is l and the number of nonlinear parameters is n φ For n φ +1 variable φ l,1 ,φ l,2 , ,φ l,nφ+1 Using the evaluation function value L(φ l,1 ), L(φ l,2 ),···,L(φ l,nφ+1 ) is calculated. Furthermore, the evaluation function values ​​are also calculated for the parameter values ​​subjected to four types of operations, namely, mirror image, enlargement, contraction, and reduction. Then, using the evaluation function values ​​calculated in this way, the parameters are adjusted according to a known algorithm, φ l From φ l+1 to update.

[0066] Thus, some nonlinear optimization methods require determining cost functions or output estimates for a number of different nonlinear parameter estimates in order to update the nonlinear parameter estimates.

[0067] Although the explanation has been omitted because it is outside the scope of the present application, even when the original problem P1 includes at least one of an equality constraint and an inequality constraint for the nonlinear parameter φ, it is possible to apply a known nonlinear optimization method with constraint conditions to update the nonlinear parameter φ. For example, a local solution can be obtained by applying the above-mentioned interior point method, sequential quadratic programming method, or the like.

[0068] The above is the content of the parameter estimation technology of the present application, which has been described for a general problem. Based on this content, a case in which this technology is applied to the storage battery 1 will be described.

[0069] <Application to storage batteries> As described in FIG. 1, the current detection device 21 detects the current of the storage battery 1 and outputs the detected current value I. The voltage detection device 22 detects the terminal voltage of the storage battery 1 and outputs the detected voltage value V. However, when the storage battery 1 is configured with a series-parallel connection of multiple cells, the detected current and voltage may be those of a single or multiple cells that are part of the storage battery 1. In the following, the sampling period of the time series data is defined as t s The explanation will be given assuming that the sampling period is t s does not have to be fixed, but may be variable.

[0070] The time series data acquisition unit 31 acquires a time series {t k The time series data of the detected current for |k=0,1,···,N} {I(t k )|k=0,1,...,N} and the time series data of the detected voltage {V(t k )|k=0,1,···,N}. For simplicity, we use the sampling period t s Considering the case where is fixed, for the initial time t0, t k =t0+kt s However, the time series data may be held internally by the time series data acquisition unit 31, or may be acquired via an external PC, server, cloud, or the like.

[0071] The model acquisition unit 32 holds a storage battery model for the storage battery 1 to be estimated, and is used in the parameter estimation unit 33. Then, parameters of the storage battery model including initial values ​​are appropriately updated based on parameters estimated by the parameter estimation unit 33. Note that the storage battery model held by the model acquisition unit 32 may be originally held inside the model parameter estimation device 3, or may be acquired from an external PC, server, cloud, etc.

[0072] As a storage battery model, for example, an equivalent circuit model as shown in Fig. 3 is used. In Fig. 3, the resistive element R0 represents the DC component of the overvoltage caused by the electrolyte resistance, collector metal resistance, contact resistance, charge transfer resistance, etc. of the storage battery 1. d and capacitor element C d represents the relaxation component of the overvoltage resulting from the diffusion component of the storage battery 1.

[0073] At this time, the state space model of the storage battery 1 is described, for example, as in equations (23) to (25).

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[0075] Here, q is the quantity of electricity, I is the detected current value (detected current), and I off is the current offset error included in the detection current, q d is the capacitor element C d The charge stored in, f OCV is a function that represents the OCV characteristic that depends on the charge q of the storage battery 1 (OCV function f OCV ) where the electric charge q may be a normalized value, in which case the OCV function f OCV is also a function of the normalized electric quantity q.

[0076] When a discrete-time state space model is used, for example, equations (23) to (25) are transformed by a zero-order hold into equations (26) to (28) and then used.

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[0078] As another storage battery model, a Foster-type equivalent circuit model in which multiple CR parallel elements are connected in series as shown in Fig. 4 may be used. The equivalent circuit model in Fig. 4 is a more detailed storage battery model than the equivalent circuit model in Fig. 3 because it has three CR parallel elements connected in series. Of course, the number of CR parallel elements connected in series may be arbitrary.

[0079] In addition, when the diffusion impedance is approximated by a Foster type circuit, each CR parallel element has a diffusion resistance R d and the diffusion capacitance C d It can be expressed as follows using only (see, for example, Kuhn, Estelle, et al. "Modelling Ni-mH battery using Cauer and Foster structures." Journal of power sources 158.2 (2006): 1490-1497.).

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[0081] In this case, equations (27) and (28) become equations (30) and (31).

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[0083] It should be noted that other models may be used as the storage battery model, for example, a Cauer type circuit may be used. Also, a so-called electrochemical model that attempts to directly describe the internal phenomenon of the storage battery 1 without using an equivalent circuit may be used. Various known models may be used as the model of the storage battery 1, and are not limited as long as they can be expressed within the framework of formula (1) or formula (3). However, for simplicity, the following description will be given assuming the equivalent circuit model described in FIG. 3.

[0084] OCV function f that represents the OCV characteristics OCV Typically, a linear or piecewise linear function is used for the electric quantity q. For example, when a polynomial is used, it is expressed as in Equation (33), and a parameter linear expression is possible.

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[0086] Alternatively, a piecewise linear function (linear spline curve) shown in equation (34) is used.

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[0088] Alternatively, a cubic spline curve of equation (36) is used.

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[0091] Alternatively, any other degree of spline curve is used.

[0092] Piecewise polynomials such as spline curves can also be expressed as parameter linear functions. As an example, piecewise linear functions can be expressed as in equation (38). Here, δ i,k is as shown in equation (39).

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[0094] Similarly, other cases such as cubic spline curves can be expressed as linear parameters. Also, other OCV functions f OCV It is also possible to consider the case where both the linear parameter ψ and the nonlinear parameter φ are included. In that case, the function form becomes as shown in equation (40).

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[0096] Other OCV functions OCV It is also possible to consider the case where only the nonlinear parameter φ is included as the OCV function f OCV The function form of is not necessarily limited to a form including the linear parameter ψ. However, when many linear parameters ψ are included, the advantage of the approach of converting problem P1 to problem P2 in this application is particularly strong. However, in the following, we will convert equation (34) into the OCV function f OCV The case where it is used as above will be described.

[0097] The nonlinear parameter update unit 331 updates the time series data of the detected current {I(t k )|k=0,1,···,N} and the time series data of the detected voltage {V(t k ) |k=0,1,···,N} and the battery model, the nonlinear parameter φ of the battery model is updated, where the nonlinear parameter φ is expressed as in Equation (41).

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[0099] Depending on how the state space model of the storage battery 1 is created, the elements of the nonlinear parameter φ may vary. For example, the OCV function f OCV The nonlinear parameter φ OCV If the nonlinear parameter φ does not include OCV In addition, the parameters included in the state equations of Eqs. (24) and (30) are the time constant τ d and the current offset error I offHowever, depending on the modeling method, other parameters may also be included in the state equation.

[0100] For example, when a multi-stage CR parallel element is expressed by approximating the diffusion impedance as in equation (29), the time constant is τ d In other cases, there will be only one parameter, i.e., time constant parameters for the number of CR parallel elements. Also, for example, if the state equation for CR overvoltage in equation (42) is used instead of the state equation for CR overvoltage in equation (24), and the output equation is equation (43) instead of equation (25), the nonlinear parameter φ is used instead of the linear parameter ψ. d Include.

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[0102] However, in this case, τ d and C. d Considering that both are included in the nonlinear parameter φ, it is better to use equation (24) in order to make the most of the advantages of the technical idea of ​​the present application.

[0103] As a specific method for updating the nonlinear parameter φ, it is possible to use a known nonlinear optimization method based on repeated calculations as described above.

[0104] A predetermined value is used as the initial value of the nonlinear parameter φ. If possible, the predetermined value is determined by prior knowledge of the true value of the nonlinear parameter φ. For example, the diffusion time constant τ d It is known that in lithium-ion batteries, the time is usually several tens to several hundreds of seconds, so the initial value is set to, for example, 100 seconds. In addition, the current offset error I off Since is a very small value, the initial value is set to, for example, 0A.

[0105] These settings are highly appropriate for general lithium-ion batteries and current sensors, and are independent of the series-parallel connection configuration of the battery 1, and therefore have the advantage in terms of product installation in that initial value tuning is not required in many cases. Also, if the results of characteristic evaluation of the battery 1 when it is new or data on a spec sheet are available, these may be used. Also, if parameter estimation has been performed in the past, the past estimation results may be used.

[0106] The initial values ​​may be set in the model acquisition unit 32, in the nonlinear parameter update unit 331, or in a separately provided initial value setting unit (not shown). In this case, the initial values ​​may be set automatically based on the above-mentioned prior knowledge, or prior information, initial value candidates, etc. may be presented via an input I / F (not shown) to prompt input, and the initial values ​​may be set based on the input.

[0107] Note that the update of the nonlinear parameter φ may include the operations of a state quantity calculation unit 332 and a linear parameter estimation unit 333, which will be described later. For example, when gradient information regarding the nonlinear parameter φ of the evaluation function is used to update the nonlinear parameter φ, calculations similar to those of the state quantity calculation unit 332 and the linear parameter estimation unit 333 are required.

[0108] The state quantity calculation unit 332 calculates the time series data of the detected current {I(t k ) |k=0,1,...,N} and the battery model, the time series values ​​of the state quantities in the battery model (i.e., the state space model of the battery 1) are calculated. For example, the state quantities in the state space model of the equations (23) to (25) are the electric quantity q and the electric charge q d Refers to...

[0109] As described above, either a continuous-time or discrete-time state space model may be used to calculate the time series values ​​of state quantities based on a state space model. In the former case, a known numerical solution method such as the fourth-order Runge-Kutta method may be used, while in the latter case, calculations may be performed sequentially according to the model. Alternatively, calculations may be performed based on the solution of the state equation.

[0110] The linear parameter estimation unit 333 estimates the time series data of the detected current {I(t k )|k=0,1,···,N} and the time series data of the detected voltage {V(t k )|k=0,1,...,N}, the battery model, and the state quantities, a linear parameter ψ is estimated, and the model output of the voltage is calculated. Specifically, since the linear parameter ψ can be expressed separately in the output equation as in equation (44), it can be expressed as in equation (45).

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[0112] Therefore, the linear least-squares solution of the linear parameters ψ for an estimated value of the nonlinear parameters φ can be estimated as equation (46). ψ(φ)=(G Τ (φ)G(φ)) -1 G Τ (φ)ν (46) Therefore, problem P1, which is a voltage error minimization problem based on the output error method in the storage battery 1, can be converted to problem P2 by equation (46). In addition, by using the estimated value of this linear parameter ψ, the model output of the voltage can also be calculated.

[0113] If equality constraints are included, problem P3 can be considered with the equality constraints taken into account. For example, if the OCV function f OCV If is a linear spline curve (piecewise linear function), it must satisfy equation (35), so ψ OCV,i =[a i b i ] Τ Then, for equation (47), the equality constraint equation becomes equation (48). χ i =[p i+1 1] Τ (47)

[0114]

number

[0115] Also, the OCV function f OCV If is a cubic spline curve, it must satisfy equation (37), so ψ OCV,i =[a i b i c i d i ] Τ Then, for equation (49), the equality constraint equation becomes equation (50).

[0116]

number

[0117] By formulating the problem in this way, it is possible to treat the problem to be solved as problem P3 and sub-problem SP3. The solution method in this case has already been described. Note that the constraint equation is not limited to the one described in the above example, and may be any single or multiple equations expressed by linear constraint equations.

[0118] It is also possible to include inequality constraints on the linear parameters ψ. For example, R0 and C d Regarding R 0,min ≦R0≦R 0,max ,C d,min ≦C d ≦C d,max If it is desired to reflect prior knowledge regarding the upper and lower limit constraints, the inequality constraints can be expressed as in equation (51).

[0119]

number

[0120] This makes it possible to treat the problem to be solved as problem P4 and sub-problem SP4. The solution method at this time has already been explained. Note that the constraint inequality is not limited to the one explained in the above example, and may be any single or multiple inequalities expressed as linear constraint inequalities.

[0121] Here, the OCV function f OCV We have explained the polynomial approximation method and spline approximation method of R0,R d ,C d , τ d The electric quantity dependency of the circuit parameters such as may be modeled. The temperature dependency of the circuit parameters may be modeled in a similar manner. However, when modeling the temperature dependency, it is necessary to separately measure the temperature of the storage battery 1, and in that case, the model parameter estimation device 3 needs to obtain the output of a temperature detector. As the temperature model, the well-known Arrhenius equation or the like may be used.

[0122] The determination unit 334 uses the time series data of the detected voltage {V(t k )|k=0,1,...,N}, the voltage model output, the linear parameter estimates, and the nonlinear parameter estimates are used to determine the convergence of the parameter estimates and voltage estimates. If a predetermined determination criterion is met, the estimation is terminated and the model parameters are output to the outside. If the determination criterion is not met, the process returns to the nonlinear parameter update unit 331 and the update of the nonlinear parameter φ is repeated.

[0123] Specifically, the j-th element of the l-th estimate of the parameter θ is θ j l Then, similarly to Patent Document 1, it is determined whether or not formula (52) is satisfied.

[0124]

number

[0125] Alternatively, it is determined whether or not equation (53) is satisfied for only the nonlinear parameter φ.

[0126]

number

[0127] Alternatively, it is determined whether or not the formula (54) is satisfied based on the root-mean-square error (RMSE) regarding the voltage.

[0128]

number

[0129] Alternatively, the judgment may be based on the mean absolute error (MAE) regarding the voltage. Alternatively, the convergence condition may be judged based on whether the number of iterations of estimating the nonlinear parameter φ has reached a predetermined upper limit. Alternatively, a composite judgment may be made using a plurality of the above methods. Alternatively, any other convergence judgment method may be used. Since various publicly known methods are known for judging the convergence of estimated parameters in nonlinear optimization, there is no limitation regarding the convergence judgment method.

[0130] The final parameter estimates from the parameter estimation unit 33 may be stored in the model acquisition unit 32 and used as initial values ​​for the next model parameter estimation, or may be stored in an external PC, server, cloud, etc.

[0131] <Processing Procedure of Model Parameter Estimation Device> Next, a processing procedure of the model parameter estimation device 3 according to the first embodiment, that is, a model parameter estimation method, will be described with reference to the flowchart in Fig. 5. However, here, the most typical case, that is, a case where a nonlinear optimization method using a gradient approximation is used, will be described.

[0132] First, the time-series data acquisition unit 31 acquires the current value I of the storage battery 1 output by the current detection device 21 and the voltage value V of the storage battery 1 output by the voltage detection device 22 as time-series data of the measured values ​​(step S1310). Next, the model acquisition unit 32 acquires a storage battery model from outside or held internally, and sets or reads the initial value of the nonlinear parameter φ (step S1320). As the storage battery model, for example, a state space model shown in equations (23) to (25) or equations (26) to (28) corresponding to equation (3) is acquired.

[0133] The acquired time-series data, storage battery model, and initial value are output to the parameter estimation unit 33, and each unit in the parameter estimation unit 33 executes the following repeated calculations (steps S2331 to S2400).

[0134] In step S2331, the nonlinear parameter update unit 331 updates the nonlinear parameter φ so that the error minimized for the linear parameter ψ becomes smaller according to a nonlinear optimization method, which is a type of gradient method based on iterative calculation. In the gradient calculation, for example, when a gradient approximation value based on one-sided difference is used, the gradient approximation value is calculated based on an output estimate value for a perturbation value for each element of the previous nonlinear parameter update value (previous value) described later. However, in the calculation of the gradient approximation value based on one-sided difference or the like, the output estimate value for the previous value is also used. Note that, at the first time, a predetermined value is set as it is as the initial value of the nonlinear parameter (for example, τ d =100, I off =0, etc.).

[0135] In step S2332, the state quantity calculation unit 332 calculates the state quantity of the storage battery model based on the state equation of the storage battery model using the updated nonlinear parameter φ. In step S2333, the linear parameter estimation unit 333 estimates the linear parameter ψ and the output value of the storage battery model based on the state quantity output from the state quantity calculation unit 332.

[0136] Then, in step S2334, the judgment unit 334 judges the convergence of the parameter estimation in the parameter estimation unit 33 according to a predetermined convergence judgment condition. If it is judged that the convergence judgment condition is satisfied ("Yes" in step S2400), the parameter estimation is terminated and the parameters of the estimation result are output to the outside. At this time, the parameters of the estimation result may be held in the model acquisition unit 32.

[0137] On the other hand, if it is determined that the convergence determination condition is not satisfied ("No" in step S2400), the process proceeds to step S3331, and the execution of each step from step S3331 onwards continues.

[0138] In step S3331, the nonlinear parameter update unit 331 sets a perturbation value for each nonlinear parameter element. In step S3332, the state quantity calculation unit 332 calculates the state quantity of the storage battery model for each perturbation value of the nonlinear parameter element based on the state equation of the storage battery model by each perturbation value of the nonlinear parameter element set by the nonlinear parameter update unit 331.

[0139] In step S3333, the linear parameter estimation unit 333 estimates the linear parameters ψ and the output values ​​of the storage battery model for each perturbation value of each nonlinear parameter element, based on the state quantities for each perturbation value of each nonlinear parameter element output from the state quantity calculation unit 332. Then, the execution of each step from step S2331 onwards described above is continued.

[0140] The above is an example of the processing procedure of the model parameter estimation device 3 according to the first embodiment, that is, an example of the operation of the model parameter estimation method. Note that the contents and order of the processing described in FIG. 5 are merely an example, and the contents and order are not limited to these.

[0141] Next, a result of applying the model parameter estimation device 3 or the model parameter estimation method according to the first embodiment to time-series data of current and voltage during operation of a certain storage battery system 100 will be described with reference to Fig. 6. In this application, the current and voltage in the storage battery system 100 with a series-parallel connection configuration are converted into cells using the storage battery 1.

[0142] Here, the model of the storage battery 1 is approximated by the Foster type circuit shown in Figure 4, and R1, R2, R3 and C1, C2, C3 follow the equation (29) that finitely approximates the diffusion impedance. In addition, the OCV function f OCV As for m s = 10 and a cubic spline curve with equal intervals was used. For simplicity, the nonlinear parameter φ is set to τ d The linear parameters ψ are R0, C d and all parameters of the cubic spline curve.

[0143] In the time series data of the current I in the upper part of Fig. 6, the first half is free charging and discharging, and the second half is constant power charging. In both cases, it can be seen that the actual data in the middle part (measured values: solid line) and the model output in the lower part (estimated values: dashed line) match with good accuracy.

[0144] In addition, the estimated OCV function f OCV is shown in Fig. 7. Note that the horizontal axis indicates a standard capacity q typ Electrical quantity q / q normalized by typ The estimation results are obtained by smoothly connecting each point while calculating the non-linear electric quantity q / q typ This model is able to model the nonlinear fluctuations in OCV with respect to the voltage. As a result, the voltage in Fig. 6 (middle row: actual data, bottom row: model output) can be estimated with high accuracy, including subtle irregularities during charging.

[0145] Embodiment 2 In the first embodiment, the processing when the OCV function is unknown is described. In the second embodiment, the processing when the OCV function is known is described. Note that the configuration of the model parameter estimation device and the basic operation of the model parameter estimation method are the same as in the first embodiment, so the description of the similar parts will be omitted and the figures used in the first embodiment will be used.

[0146] OCV function f OCV is known, in the state space model of the storage battery 1 expressed by equations (23) to (25), equation (25) expresses the full charge capacity q max This can be expressed as equation (55) using

[0147]

number

[0148] Moreover, if the output equation is transformed, it becomes as in equation (57), and since it can be expressed in a parameter linear manner as in the first embodiment, the linear parameter ψ becomes as in equation (58).

[0149]

number

[0150] Also, the OCV function f OCV For more detailed information, the positive electrode potential function f p and the negative electrode potential function f n is known, and the OCV function f OCVcan be expressed using the electrode parameters as in equation (59).

[0151]

number

[0152] In this case, the OCV function f OCV By modeling in more detail, it is possible to diagnose the deterioration of the storage battery 1 in more detail. Specifically, it is possible to distinguish and grasp the decrease in the positive electrode capacity, the decrease in the negative electrode capacity, and the difference in the electric charge between the positive electrode and the negative electrode that accompanies the deterioration of the storage battery 1. The difference in the electric charge between the positive electrode and the negative electrode is said to be a phenomenon that occurs mainly due to the growth of the coating (SEI: Solid Electrolyte Interface) formed on the surface of the negative electrode and the deposition of lithium, and causes a decrease in the full charge capacity of the storage battery 1.

[0153] As described above, in the model parameter estimation device 3 or model parameter estimation method of the present application, the update of the nonlinear parameter φ and the estimation of the linear parameter ψ are separated. Alternatively, the nonlinear parameter φ is updated by considering a problem in which a linear least-squares solution of the linear parameters is embedded, such as problem P2. This has three major advantages during optimization calculation, as described above.

[0154] First, the initial value dependency is reduced because the initial value needs to be set only for the nonlinear parameter φ. Second, the amount of calculation is reduced. Third, numerical stability is improved.

[0155] In estimating the linear parameter ψ, it is possible to obtain optimal solutions for unconstrained linear least squares problems, linear least squares problems with linear equality constraints, and linear inequality constraint problems. In particular, for unconstrained linear least squares problems, a linear least squares solution can be obtained without iterative calculations. Also, for linear least squares problems with linear equality constraints, a global optimal solution can be obtained without iterative calculations by using the Lagrange multiplier method.

[0156] These advantages are more effective when the battery model is complicated and the number of parameters to be estimated increases. Therefore, it is also useful for more detailed modeling and deterioration diagnosis by estimating some or all of the electrode parameters after separately storing the positive electrode potential characteristics and the negative electrode potential characteristics as the OCV characteristics stored in advance.

[0157] Here, if we reconsider the continuous-time system identification method based on the output error method described in Patent Document 1, although OCV characteristic data is not required, the method for estimating model parameters in the case where OCV characteristic data is not available is not specified. In practical use, model parameter estimation technology that does not assume OCV characteristic data is also important. For example, since it is known that OCV characteristics fluctuate due to degradation, etc., it is important to estimate model parameters including OCV characteristics in order to improve the accuracy of estimation and apply it to deterioration diagnosis.

[0158] Furthermore, in the reuse of storage batteries, modeling may be required under circumstances where there is no or little prior information on the true values ​​of model parameters including the OCV characteristics. When the OCV characteristics are parameterized by a certain function and are included in the model parameters for collective estimation, the method described in Patent Document 1 has the above-mentioned problems with initial value setting and convergence, making it more difficult to converge to the optimal value.

[0159] In contrast, in the present application, the OCV characteristics, which are the relationship between the quantity of electricity (which may be SOC or a normalized quantity of electricity) and the OCV, are expressed as a function including parameters, and the parameters are then estimated, making it possible to estimate the OCV characteristics even if they are unknown.

[0160] In particular, if expressed as a function including many linear parameters ψ, such as a polynomial or piecewise polynomial, the feature of the present invention, which separates the process of updating the nonlinear parameters φ from the process of estimating the linear parameters ψ, can be utilized. This makes it possible to easily estimate all parameters without the need to carefully set the initial values ​​of the many linear parameters ψ. Also, as described above, a global solution can be obtained in estimating the linear parameters ψ even if linear equality constraints are included, so that the OCV function f can be expressed as a piecewise polynomial including linear equality constraints. OCV It is possible to easily estimate parameters even when dealing with a curve with a local variation. By using a piecewise polynomial instead of a polynomial, it becomes easier to accurately express the curve, including local variations.

[0161] In addition, although various exemplary embodiments and examples are described in this application, various features, aspects, and functions described in one or more embodiments are not limited to application of a specific embodiment, but can be applied to the embodiments alone or in various combinations. Therefore, countless modifications not illustrated are expected within the scope of the technology disclosed in this specification. For example, this includes cases where at least one component is modified, added, or omitted, and further, cases where at least one component is extracted and combined with components of other embodiments.

[0162] As described above, according to the model parameter estimation device 3 of the present application, the state of the storage battery 1 with respect to the measured value of the current value I (e.g., the quantity of electricity q, the charge q) is estimated based on a state equation obtained by substituting a value (e.g., an initial value) for the nonlinear parameter φ in the state space model expressing the storage battery 1 using the nonlinear parameter φ and the linear parameter ψ, and on time-series data of the measured values ​​of the current (current value I) and the terminal voltage (voltage value V) of the storage battery 1. d The system is configured to include a state quantity calculation unit 332 that calculates a state quantity indicating (i.e., a state quantity indicating the state of the nonlinear parameter φ), a linear parameter estimation unit 333 that estimates a linear parameter ψ that minimizes the error between the measured voltage value V and an estimated value of the voltage value V, the value being calculated based on a state space model, the state quantity, and the measured value of the current value I, a determination unit 334 that determines whether the estimated linear parameter ψ has converged, and a nonlinear parameter update unit 331 that repeatedly updates the value of the nonlinear parameter φ until a predetermined convergence condition is satisfied so that the minimized error becomes small, until the determination unit 334 determines that convergence has occurred. Therefore, by limiting the initial value setting to only the nonlinear parameter φ, it is possible to estimate parameters with little information.

[0163] In addition, the dependence on the initial value can be reduced, the amount of calculation can be reduced, and numerical stability can be improved. In this case, since the initial value can be a generally known value with high validity for the storage battery, it is possible to estimate without additional information when updating the system.

[0164] In particular, the nonlinear parameter update unit 331 can easily converge by updating the value of the nonlinear parameter φ using a gradient or gradient approximation of the estimated value of the voltage value V with respect to the nonlinear parameter φ, or by using a gradient-free nonlinear optimization method.

[0165] Alternatively, when updating the value of the nonlinear parameter φ, the nonlinear parameter updating unit 331 generates a perturbation value of each nonlinear parameter φ by perturbing the previous value, which is the value before the update, the state quantity calculation unit 332 calculates a state quantity for each perturbation value, the linear parameter estimation unit 333 estimates a linear parameter ψ for the state quantity for each perturbation value, and the nonlinear parameter updating unit 331 calculates a gradient approximation for the nonlinear parameter φ of the estimated value of the terminal voltage (voltage value V) based on at least the estimated value of the linear parameter ψ for the state quantity for each perturbation value, and updates the previous value based on the calculated gradient approximation, thereby ensuring more reliable convergence.

[0166] In these cases, the nonlinear parameter φ is the charge rate and full charge capacity q of the storage battery 1. max and the diffusion time constant τ d and the offset current (current offset error I off ) and the linear parameter ψ is the DC resistance of the storage battery 1 and the diffusion resistance R d If at least one of the capacitance of the capacitor is included, the state of the storage battery 1 can be reliably evaluated.

[0167] In such cases, if the linear parameter estimation unit 333 estimates the linear parameters ψ using a linear least-squares solution to a linear least-squares problem, the amount of calculation can be reduced.

[0168] In this case, the state space model includes an OCV function f that expresses the relationship between the electric quantity q and the open circuit voltage and includes a linear parameter ψ. OCV By including the above, the battery 1 can be accurately modeled.

[0169] Furthermore, the OCV function f OCV is a polynomial of the electrical quantity q, and the linear parameter ψ can model the nonlinear variation of the OCV with respect to the electrical quantity q by including a coefficient of the polynomial.

[0170] If the state space model includes a linear equality constraint on the linear parameter ψ, and the linear parameter estimation unit 333 is configured to estimate the linear parameter ψ by solving a linear least-squares problem including the linear equality constraint by the Lagrange multiplier method, convergence can be ensured by alternately repeating the update of the nonlinear parameter φ and the calculation of the linear parameter ψ by the Lagrange multiplier method.

[0171] The state space model expresses the relationship between the electrical quantity q and the open circuit voltage, and is expressed as the OCV function f OCV where the linear parameters ψ include linear parameters of the piecewise polynomial, and the linear equality constraints include linear equality constraints at the nodes of the piecewise polynomial, then it is possible to fully utilize the feature of the present application that separates the processes of updating the nonlinear parameters φ and estimating the linear parameters ψ.

[0172] Alternatively, the state space model may include a linear inequality constraint on the linear parameter ψ, and the linear parameter estimation unit 333 may be configured to estimate the linear parameter ψ by solving a linear least squares problem including the linear inequality constraint, thereby obtaining an optimal solution.

[0173] The state space model includes OCV characteristic information that represents the relationship between the charge rate and the open circuit voltage of the storage battery 1, and the nonlinear parameter φ is a full charge capacity q max By including the above, the deterioration of the storage battery 1 can be diagnosed in detail.

[0174] In this case, the state space model includes positive electrode potential characteristic information representing the relationship between the positive electrode electric quantity and the positive electrode potential of the storage battery 1, and negative electrode potential characteristic information representing the relationship between the negative electrode electric quantity and the negative electrode potential of the storage battery 1, and the nonlinear parameter φ is a full charge capacity q max Instead, if at least one of the positive electrode capacity, the negative electrode capacity, the positive electrode electric quantity, and the negative electrode electric quantity is included, the deterioration of the storage battery 1 can be diagnosed in more detail.

[0175] According to the model parameter estimation method of the present application, a step (S1320) of setting an initial value of a nonlinear parameter φ of a state space model expressing the storage battery 1 using a nonlinear parameter φ and a linear parameter ψ, a state equation obtained by substituting a value for the nonlinear parameter φ for the state space model, and a time series data of the measured values ​​of the current (current value I) and terminal voltage (voltage value V) of the storage battery 1 are used to estimate the state of the storage battery (e.g., the quantity of electricity q, the charge q d The method includes a state quantity calculation step (S2332) of calculating a state quantity indicating (V), a linear parameter estimation step (S2333) of estimating a linear parameter ψ that minimizes the error between the estimated value of the voltage value V calculated based on the state space model, the state quantity, and the measured value of the current value I, and the measured value of the voltage value V, a determination step (S2334) of determining whether the estimated linear parameter ψ has converged, and a nonlinear parameter update step (S2331) of repeatedly updating the value of the nonlinear parameter ψ until it is determined that the linear parameter ψ has converged and a predetermined convergence condition is satisfied so that the minimized error becomes small. Therefore, the initial value setting is limited to only the nonlinear parameter ψ, so that the parameters can be estimated with less information.

[0176] In addition, the dependence on the initial value can be reduced, the amount of calculation can be reduced, and numerical stability can be improved. In this case, since the initial value can be a generally known value with high validity for the storage battery, it is possible to estimate without additional information when updating the system.

[0177] In the nonlinear parameter updating step (S2331), the value of the nonlinear parameter φ can be easily converged by updating the value using the gradient or gradient approximation of the estimated value of the voltage value V for the nonlinear parameter φ, or by using a gradient-free nonlinear optimization method.

[0178] Alternatively, when updating the value of the nonlinear parameter φ, the method further includes a perturbation value setting step (S3331) for generating perturbation values ​​of each of the nonlinear parameters φ (elements) by perturbing the previous value, which is the value before the update, a perturbation state quantity calculation step (S3332) for calculating a state quantity for each perturbation value, and a perturbation linear parameter estimation step (S3333) for estimating a linear parameter ψ for the state quantity for each perturbation value, and the nonlinear parameter updating step (S2331) is configured to calculate a gradient approximation for the nonlinear parameter φ of the estimated value of the terminal voltage (voltage value V) based on at least the estimated values ​​of the linear parameters for the state quantities for each perturbation value, and to update the previous value based on the calculated gradient approximation, thereby ensuring convergence.

[0179] In these cases, the nonlinear parameter φ is the charge rate and full charge capacity q of the storage battery 1. max and the diffusion time constant τ d and the offset current (current offset error I off ) and the linear parameter ψ is the DC resistance of the storage battery 1 and the diffusion resistance R d If at least one of the capacitance of the capacitor is included, the state of the storage battery 1 can be reliably evaluated.

[0180] In the linear parameter estimation step (S2333), if the linear parameters ψ are estimated using a linear least-squares solution to the linear least-squares problem, the amount of calculations can be reduced.

[0181] In this case, the state space model includes an OCV function f that expresses the relationship between the electric quantity q and the open circuit voltage and includes a linear parameter ψ. OCV By including the above, the battery 1 can be accurately modeled.

[0182] Furthermore, the OCV function f OCV is a polynomial of the electrical quantity q, and the linear parameter ψ can model the nonlinear variation of the OCV with respect to the electrical quantity q by including a coefficient of the polynomial.

[0183] If the state space model includes a linear equality constraint on the linear parameter ψ, and the linear parameter estimation step (S2333) is configured to estimate the linear parameter ψ by solving a linear least-squares problem including the linear equality constraint using the Lagrange multiplier method, convergence can be ensured by alternately repeating the updating of the nonlinear parameter φ and the calculation of the linear parameter ψ using the Lagrange multiplier method.

[0184] The state space model expresses the relationship between the electrical quantity q and the open circuit voltage, and is expressed as the OCV function f OCV where the linear parameters ψ include linear parameters of the piecewise polynomial, and the linear equality constraints include linear equality constraints at the nodes of the piecewise polynomial, then it is possible to fully utilize the feature of the present application that separates the processes of updating the nonlinear parameters φ and estimating the linear parameters ψ.

[0185] Alternatively, the state space model may be configured to include a linear inequality constraint on the linear parameters ψ, and the linear parameter estimation step (S2333) may be configured to estimate the linear parameters ψ by solving a linear least squares problem including the linear inequality constraint, thereby making it possible to obtain an optimal solution.

[0186] The state space model includes OCV characteristic information that represents the relationship between the charge rate and the open circuit voltage of the storage battery 1, and the nonlinear parameter φ is a full charge capacity q max By including the above, the deterioration of the storage battery 1 can be diagnosed in detail.

[0187] In this case, the state space model includes positive electrode potential characteristic information representing the relationship between the positive electrode electric quantity and the positive electrode potential of the storage battery 1, and negative electrode potential characteristic information representing the relationship between the negative electrode electric quantity and the negative electrode potential of the storage battery 1, and the nonlinear parameter φ is a full charge capacity q max Instead, if at least one of the positive electrode capacity, the negative electrode capacity, the positive electrode electric quantity, and the negative electrode electric quantity is included, the deterioration of the storage battery 1 can be diagnosed in more detail. [Explanation of symbols]

[0188] 1: storage battery, 21: current detection device, 22: voltage detection device, 3: model parameter estimation device, 31: time series data acquisition unit, 32: model acquisition unit, 33: parameter estimation unit, 331: nonlinear parameter update unit, 332: state quantity calculation unit, 333: linear parameter estimation unit, 334: judgment unit, I: current value, I off : current offset error, q: electrical quantity, q max : Full charge capacity, R d : diffusion resistance, V: voltage value, τ d : Diffusion time constant.

Claims

1. a state quantity calculation unit that calculates a state quantity indicating a state of the target system with respect to a measured value of the input, based on a state equation obtained by substituting values ​​for the nonlinear parameters in a state space model that expresses the target system using nonlinear parameters and linear parameters, and based on time-series data of the measured values ​​of each of the inputs and outputs of the target system; a linear parameter estimating unit that estimates the linear parameters that minimize an error between an estimated value of an output calculated based on the state space model, the state quantity, and the measured value of the input, and the measured value of the output; and a nonlinear parameter update unit that repeatedly updates the values ​​of the nonlinear parameters until a predetermined convergence condition is satisfied so that the minimized error becomes smaller; A model parameter estimation device comprising:

2. 2. The model parameter estimation device according to claim 1, wherein the state quantity calculation unit calculates the state quantity assuming that the target system is a storage battery, the input is a current of the storage battery, and the output is a terminal voltage of the storage battery.

3. 3. The model parameter estimation device according to claim 1, wherein the nonlinear parameter update unit updates the values ​​of the nonlinear parameters by utilizing a gradient or a gradient approximation of the estimated value of the output with respect to the nonlinear parameters, or by using a gradient-free nonlinear optimization method.

4. the nonlinear parameter update unit generates perturbation values ​​of the nonlinear parameters by perturbing previous values, which are values ​​before the update, when updating the values ​​of the nonlinear parameters; the state quantity calculation unit calculates a state quantity for each of the perturbation values; the linear parameter estimation unit estimates linear parameters for the state quantity for each of the perturbation values; The nonlinear parameter update unit calculates a gradient approximation value for the nonlinear parameter of the estimated value of the output based on an estimate value of the linear parameter for the state quantity for at least each of the perturbation values, and updates the previous value based on the calculated gradient approximation value.

3. The model parameter estimation device according to claim 1 or 2.

5. the nonlinear parameters include at least one of a charging rate, a full charge capacity, a diffusion time constant, and an offset current of a sensor used to measure the current of the storage battery; 3. The model parameter estimation device according to claim 2, wherein the linear parameters include at least one of a DC resistance, a diffusion resistance, and a capacitance of the storage battery.

6. 3. The model parameter estimation device according to claim 2, wherein the linear parameter estimation unit estimates the linear parameters using a linear least-squares solution of a linear least-squares problem.

7. 7. The model parameter estimation device according to claim 6, wherein the state space model includes an OCV function that represents a relationship between an electrical quantity and an open circuit voltage and that includes the linear parameters.

8. the OCV function is a polynomial of the electrical quantity, 8. The apparatus of claim 7, wherein the linear parameters include coefficients of the polynomial.

9. the state space model includes linear equality constraints on the linear parameters; 6. The model parameter estimation device according to claim 2, wherein the linear parameter estimation unit estimates the linear parameters by solving a linear least squares problem including the linear equality constraints by a Lagrange multiplier method.

10. The state space model includes an OCV function that represents a relationship between an electrical quantity and an open circuit voltage and is a piecewise polynomial function including the linear parameters; the linear parameters include linear parameters of the piecewise polynomial; 10. The model parameter estimator of claim 9, wherein the linear equality constraints include linear equality constraints at the knots of the piecewise polynomial.

11. the state space model includes linear inequality constraints on the linear parameters; 3. The model parameter estimation device according to claim 1, wherein the linear parameter estimation unit estimates the linear parameters by solving a linear least squares problem including the linear inequality constraint.

12. the state space model includes OCV characteristic information representing a relationship between a charging rate and an open circuit voltage of the storage battery; 7. The model parameter estimation device according to claim 2, wherein the nonlinear parameters include a full charge capacity.

13. the state space model includes positive electrode potential characteristic information representing a relationship between a positive electrode electric quantity and a positive electrode potential of the storage battery, and negative electrode potential characteristic information representing a relationship between a negative electrode electric quantity and a negative electrode potential of the storage battery, 13. The model parameter estimation device according to claim 12, wherein the nonlinear parameters include at least one of a positive electrode capacity, a negative electrode capacity, a positive electrode electric quantity, and a negative electrode electric quantity, instead of the full charge capacity.

14. A step of setting initial values ​​of nonlinear parameters of a state space model that represents a target system using nonlinear parameters and linear parameters; a state quantity calculation step of calculating a state quantity indicating a state of the target system with respect to the measured value of the input, based on a state equation obtained by substituting values ​​for the nonlinear parameters for the state space model and time-series data of the measured values ​​of the input and output of the target system; a linear parameter estimation step of estimating the linear parameters that minimize an error between the estimated value of the output calculated based on the state space model, the state quantity, and the measured value of the input, and the measured value of the output; and a nonlinear parameter updating step of repeatedly updating the values ​​of the nonlinear parameters until a predetermined convergence condition is satisfied so that the minimized error becomes smaller; A method for estimating model parameters, comprising:

15. 15. The model parameter estimation method according to claim 14, wherein, in the step of setting the initial value, the initial value is set assuming that the target system is a storage battery, and, in the step of calculating the state quantity, the state quantity is calculated assuming that the input is a current of the storage battery and the output is a terminal voltage of the storage battery.

16. 16. The method for estimating model parameters according to claim 14 or 15, wherein in the nonlinear parameter updating step, values ​​of the nonlinear parameters are updated using a gradient or a gradient approximation of the estimated value of the output for the nonlinear parameters, or using a gradient-free nonlinear optimization technique.

17. the nonlinear parameters include at least one of a charging rate, a full charge capacity, a diffusion time constant, and an offset current of a sensor used to measure the current of the storage battery; 16. The method of claim 15, wherein the linear parameters include at least one of a DC resistance, a diffusion resistance, and a capacitance of the storage battery.

18. the state space model includes linear inequality constraints on the linear parameters; 16. The model parameter estimation method according to claim 14, wherein in the linear parameter estimation step, the linear parameters are estimated by solving a linear least squares problem including the linear inequality constraint.

19. the state space model includes OCV characteristic information representing a relationship between a charging rate and an open circuit voltage of the storage battery; 16. The method of claim 15, wherein the non-linear parameters include a full charge capacity.

20. the state space model includes positive electrode potential characteristic information representing a relationship between a positive electrode electric quantity and a positive electrode potential of the storage battery, and negative electrode potential characteristic information representing a relationship between a negative electrode electric quantity and a negative electrode potential of the storage battery, 20. The method for estimating model parameters according to claim 19, wherein the nonlinear parameters include at least one of a positive electrode capacity, a negative electrode capacity, a positive electrode electric quantity, and a negative electrode electric quantity, instead of the full charge capacity.

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